curve #1936

y² + y = x³ + x² − 24791434545122407462176574410341851245x + 47463673909255798147742316846176526846664068435304032999

a-invariants: [0, 1, 1, -24791434545122407462176574410341851245, 47463673909255798147742316846176526846664068435304032999]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/3ℤ
conductor (N): 5461276154000123738982180117457943018064043018715 ☆ record for ℤ/3ℤ torsion, rank ≥ 14
discriminant (Δ): 1970615313009539827626299562147832780455069444284501713614252214316563615474927456974285235339052865480189453125 ☆ record for ℤ/3ℤ torsion, rank ≥ 14
Faltings height: 20.2675 ☆ record for ℤ/3ℤ torsion, rank ≥ 14
naive height: 269.9243 ☆ record for ℤ/3ℤ torsion, rank ≥ 14
primes of bad reduction: 5, 19, 23, 29, 43, 61, 73, 139, 307, 331, 397, 439, 3307, 3907, 4957, 5323, 99859, 282679
regulator: 166466685524891.897263920270076954760849183280244689564558377709113
submitted by: dujella
submitted at: 2026-09-25 19:34:25 UTC
last updated: 2026-09-25 19:34:25 UTC

(3045140793366361281, 455519346190208924256293612)
(-528216676545090209, 7772486334965581899275176132)
(2203920316828156637, 1878923129661099866370805107)
(2949565141361554893, 27319813023963716607265779)
(2082360557357435101, 2206479862158999933236306572)
(3418925429587448731, 1633279503594310209884293012)
(3008880827154416631, 331201878306635437696852187)
(-731297975613141829, 8074806749345022438871193067)
(2787230928945927881, 131376375535040254079887187)
(3756970281368687881, 2711451964147031600152527187)
(202374556341695155861/81, 771315701029785672999504179948/729)
(87853802467691849341/36, 264253862993427486286969158017/216)
(2799466327651303381, 18387620641344154427691187)
(3617621200737169131, 2263211419824045143602502187)

found by Elkies - Klagsbrun (2020)

last edited by dujella at 2026-09-25 19:34:25 UTC · history